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- https://math.libretexts.org/Courses/Las_Positas_College/Book%3A_College_Algebra/05%3A_Exponential_and_Logarithmic_Functions/5.03%3A_Graphs_of_Exponential_FunctionsAs we discussed in the previous section, exponential functions are used for many real-world applications such as finance, forensics, computer science, and most of the life sciences. Working with an eq...As we discussed in the previous section, exponential functions are used for many real-world applications such as finance, forensics, computer science, and most of the life sciences. Working with an equation that describes a real-world situation gives us a method for making predictions. Most of the time, however, the equation itself is not enough. We learn a lot about things by seeing their pictorial representations, and that is exactly why graphing exponential equations is a powerful tool.
- https://math.libretexts.org/Bookshelves/Algebra/Algebra_and_Trigonometry_1e_(OpenStax)/06%3A_Exponential_and_Logarithmic_Functions/6.02%3A_Graphs_of_Exponential_FunctionsAs we discussed in the previous section, exponential functions are used for many real-world applications such as finance, forensics, computer science, and most of the life sciences. Working with an eq...As we discussed in the previous section, exponential functions are used for many real-world applications such as finance, forensics, computer science, and most of the life sciences. Working with an equation that describes a real-world situation gives us a method for making predictions. Most of the time, however, the equation itself is not enough. We learn a lot about things by seeing their pictorial representations, and that is exactly why graphing exponential equations is a powerful tool.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_333%3A_Introduction_to_College_Algebra/06%3A_Exponential_and_Logarithmic_Functions/6.02%3A_Graphs_of_Exponential_FunctionsWorking with an equation that describes a real-world situation gives us a method for making predictions. Most of the time, however, the equation itself is not enough. We learn a lot about things by se...Working with an equation that describes a real-world situation gives us a method for making predictions. Most of the time, however, the equation itself is not enough. We learn a lot about things by seeing their pictorial representations, and that is exactly why graphing exponential equations is a powerful tool. It gives us another layer of insight for predicting future events.
- https://math.libretexts.org/Bookshelves/Algebra/College_Algebra_1e_(OpenStax)/06%3A_Exponential_and_Logarithmic_Functions/6.03%3A_Graphs_of_Exponential_FunctionsWorking with an equation that describes a real-world situation gives us a method for making predictions. Most of the time, however, the equation itself is not enough. We learn a lot about things by se...Working with an equation that describes a real-world situation gives us a method for making predictions. Most of the time, however, the equation itself is not enough. We learn a lot about things by seeing their pictorial representations, and that is exactly why graphing exponential equations is a powerful tool. It gives us another layer of insight for predicting future events.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_370%3A_Precalculus/01%3A_Relations_and_Functions/1.07%3A_TransformationsThis section covers transformations of functions, including translations, reflections, stretches, and compressions. It explains how to apply these transformations to function graphs and how changes in...This section covers transformations of functions, including translations, reflections, stretches, and compressions. It explains how to apply these transformations to function graphs and how changes in function equations affect their graphs. The section provides examples and visual aids to illustrate vertical and horizontal shifts, reflections over the axes, and scaling of graphs. These concepts help understand how functions can be manipulated to model different real-world scenarios.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_373%3A_Trigonometry_for_Calculus/05%3A_Graphs_of_the_Trigonometric_Functions/5.03%3A_Rigid_TransformationsThis section explores rigid transformations of trigonometric function graphs, focusing on phase shifts (horizontal shifts) and vertical shifts. It explains how to determine the new position of the gra...This section explores rigid transformations of trigonometric function graphs, focusing on phase shifts (horizontal shifts) and vertical shifts. It explains how to determine the new position of the graph based on these transformations and provides examples to illustrate the concepts. The section includes practical applications of these transformations and highlights how to graph trigonometric functions with vertical and horizontal shifts.
- https://math.libretexts.org/Courses/Angelo_State_University/Finite_Mathematics/03%3A_Functions/3.06%3A_Transformation_of_FunctionsOften when given a problem, we try to model the scenario using mathematics in the form of words, tables, graphs, and equations. One method we can employ is to adapt the basic graphs of the toolkit fun...Often when given a problem, we try to model the scenario using mathematics in the form of words, tables, graphs, and equations. One method we can employ is to adapt the basic graphs of the toolkit functions to build new models for a given scenario. There are systematic ways to alter functions to construct appropriate models for the problems we are trying to solve.
- https://math.libretexts.org/Courses/Chabot_College/Chabot_College_College_Algebra_for_BSTEM/06%3A_Exponential_and_Logarithmic_Functions/6.02%3A_Graphs_of_Exponential_FunctionsWorking with an equation that describes a real-world situation gives us a method for making predictions. Most of the time, however, the equation itself is not enough. We learn a lot about things by se...Working with an equation that describes a real-world situation gives us a method for making predictions. Most of the time, however, the equation itself is not enough. We learn a lot about things by seeing their pictorial representations, and that is exactly why graphing exponential equations is a powerful tool. It gives us another layer of insight for predicting future events.
- https://math.libretexts.org/Courses/Reedley_College/College_Algebra_1e_(OpenStax)/06%3A_Exponential_and_Logarithmic_Functions/6.02%3A_Graphs_of_Exponential_FunctionsWorking with an equation that describes a real-world situation gives us a method for making predictions. Most of the time, however, the equation itself is not enough. We learn a lot about things by se...Working with an equation that describes a real-world situation gives us a method for making predictions. Most of the time, however, the equation itself is not enough. We learn a lot about things by seeing their pictorial representations, and that is exactly why graphing exponential equations is a powerful tool. It gives us another layer of insight for predicting future events.
- https://math.libretexts.org/Courses/Palo_Alto_College/College_Algebra/02%3A_Functions/2.06%3A_Transformation_of_FunctionsOften when given a problem, we try to model the scenario using mathematics in the form of words, tables, graphs, and equations. One method we can employ is to adapt the basic graphs of the toolkit fun...Often when given a problem, we try to model the scenario using mathematics in the form of words, tables, graphs, and equations. One method we can employ is to adapt the basic graphs of the toolkit functions to build new models for a given scenario. There are systematic ways to alter functions to construct appropriate models for the problems we are trying to solve.
- https://math.libretexts.org/Courses/Palo_Alto_College/College_Algebra/04%3A_Exponential_and_Logarithmic_Functions/4.03%3A_Graphs_of_Exponential_FunctionsWorking with an equation that describes a real-world situation gives us a method for making predictions. Most of the time, however, the equation itself is not enough. We learn a lot about things by se...Working with an equation that describes a real-world situation gives us a method for making predictions. Most of the time, however, the equation itself is not enough. We learn a lot about things by seeing their pictorial representations, and that is exactly why graphing exponential equations is a powerful tool. It gives us another layer of insight for predicting future events.
